30a^2-114a+108=

Solution for 30a^2-114a+108= equation:

Simplifying
30a2 + -114a + 108 = 0

Reorder the terms:
108 + -114a + 30a2 = 0

Solving
108 + -114a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -19a + 5a2) = 0

Factor a trinomial.
6((9 + -5a)(2 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(9 + -5a)' equal to zero and attempt to solve:

Simplifying
9 + -5a = 0

Solving
9 + -5a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -5a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5a = 0 + -9
-5a = 0 + -9

Combine like terms: 0 + -9 = -9
-5a = -9

Divide each side by '-5'.
a = 1.8

Simplifying
a = 1.8
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {1.8, 2}